At a track meet 2/5 of the first place finishers went to Ohio State. One half of Ohio State's first place finishers were women. If 2/9 of the first place finishers who did NOT attend Ohio State were women, what fractional part of the total number of first place finishers were men?

Question

Mathematics

Diana Gross

11 April, 21:18

At a track meet 2/5 of the first place finishers went to Ohio State. One half of Ohio State's first place finishers were women. If 2/9 of the first place finishers who did NOT attend Ohio State were women, what fractional part of the total number of first place finishers were men?

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Answers (1)

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Messiah Hoffman · Answer 1

2/3

Step-by-step explanation:

The first place finishers can be divided into two groups: those who went to Ohio State, and those who did not attend Ohio State.

2/5 of the first place finishers went to Ohio State. 1/2 of these were women, which means 1/2 were men. The fraction of first place finishers who went to Ohio State AND were men is:

1/2 (2/5) = 1/5

3/5 of the first place finishers did not attend Ohio State. 2/9 of these were women, which means 7/9 were men. The fraction of first place finishers who did not attend Ohio State AND were men is:

7/9 (3/5) = 7/15

So the fraction of first place finishers who were men is:

1/5 + 7/15

= 3/15 + 7/15

= 10/15

= 2/3